Question 3 Let B = {4, 8, 12, 16} Consider the universal statement, Vn € B, 4| n. (Wait - we need a sidetrack lesson here. We have new notation. In this context, the symbol "|" means "divides." For example, 2 | 6 means "2 divides 6" or equivalently "6 is divisible by 2." By the way the statement 2 | 6 is true. Why? Because 6 = 2.3. Notice that we show "divides" is true with multiplication not division. Also, notice that the divides symbol "|" is vertical and not slanted like a division symbol.) a. Write one way to say the given statement out loud. b. Show that the statement is true.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 3
Let B = {4, 8, 12, 16}
Consider the universal statement, Vn € B, 4| n.
(Wait - we need a sidetrack lesson here. We have new notation. In this context, the symbol "|" means
"divides." For example, 2 | 6 means "2 divides 6" or equivalently "6 is divisible by 2." By the way the statement
2 | 6 is true. Why? Because 6 = 2.3. Notice that we show "divides" is true with multiplication not division.
Also, notice that the divides symbol "|" is vertical and not slanted like a division symbol.)
a. Write one way to say the given statement out loud.
b. Show that the statement is true.
Transcribed Image Text:Question 3 Let B = {4, 8, 12, 16} Consider the universal statement, Vn € B, 4| n. (Wait - we need a sidetrack lesson here. We have new notation. In this context, the symbol "|" means "divides." For example, 2 | 6 means "2 divides 6" or equivalently "6 is divisible by 2." By the way the statement 2 | 6 is true. Why? Because 6 = 2.3. Notice that we show "divides" is true with multiplication not division. Also, notice that the divides symbol "|" is vertical and not slanted like a division symbol.) a. Write one way to say the given statement out loud. b. Show that the statement is true.
Expert Solution
Step 1

(a) The given statement is 

         B, 4 | n. 

     This can be equivalently expressed as per the given definition of "|" as, 

        B,  n = 4.k for some integer k. 

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